A Synoptic–Dynamic Model of Subseasonal Atmospheric ...

A Synoptic–Dynamic Model of Subseasonal Atmospheric Variability

KLAUS WEICKMANN

Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado

EDWARD BERRY

National Oceanic and Atmospheric Administration/National Weather Service, Dodge City, Kansas

(Manuscript received 5 October 2005, in final form 3 May 2006)

ABSTRACT

A global synoptic–dynamic model (GSDM) of subseasonal variability is proposed to provide a frameworkfor real-time weather–climate monitoring and to assist with the preparation of medium-range (e.g., week1–3) predictions. The GSDM is used with a regional focus over North America during northern winter. Acase study introduces the time scales of the GSDM and illustrates two circulation transitions related toeastward-moving wave energy signals and their connection to remote tropical forcing. Global and zonalatmospheric angular momentum (AAM) is used to help define the synoptic evolution of the GSDMcomponents and to link regional synoptic variations with physical processes like the global mountain andfrictional torque. The core of the GSDM consists of four stages based on the Madden–Julian oscillation(MJO) recurrence time. Additionally, extratropical behaviors including teleconnection patterns, barocliniclife cycles, and �monthly oscillations provide intermediate and fast time scales that are combined with thequasi-oscillatory (30–70 day) MJO to define multiple time-/space-scale linear relationships. A unique fea-ture of the GSDM is its focus on global and regional circulation transitions and the related extreme weatherevents during periods of large global AAM tendency.

1. Introduction

Background

Synoptic models of atmospheric phenomena and dy-namical or physical processes have been used exten-sively to communicate the results of diagnostic researchand to help develop the science and art of weatherforecasting. The extratropical cyclone and its baroclin-ic–barotropic life cycle is the most well known subjectof synoptic modeling in meteorology. It has been stud-ied with numerical models and observed datasets formore than 70 yr (e.g., Bjerknes 1919; Rossby 1941; Sha-piro and Gronas 1999). Coherent and easily recognized,the behavior of baroclinic waves is the “bread and but-ter” of short-term prediction models, which have verygood forecast skill in the 1–3-day range, at least onaverage (Simmons and Hollingsworth 2002).

No comparable synoptic model exists for subseasonal(3–90 days) variability and medium-range predictions.In fact, several additions to the baroclinic life cyclemodel would be required to construct a “useful” me-dium-range synoptic model. For one, the regional do-main of the short-term prediction problem is no longeradequate for the medium range (e.g., Smagorinsky1967). Wave packets or other organized atmosphericenergy pulses can spread signals from regional tropical-extratropical interactions around the hemisphere in�10 days (Chang 1993, 1999a,b). The inherent scales ofmotion are also larger, in particular encompassingzonal wavenumbers 0–3. In the time domain, the modelshould consist of multiple time scales and their interac-tions in time and space. In terms of coherent phenom-ena, the quasi-oscillatory Madden–Julian oscillation(MJO; Madden and Julian 1971, 1972, 1994) is a viablecandidate to provide structure to a global subseasonalsynoptic model in the same way that El Niño–SouthernOscillation (ENSO) does for interannual variability.But the MJO is far from adequate by itself. Extratro-pical phenomena must also be included.

Corresponding author address: Dr. Klaus Weickmann, PhysicalSciences Division, NOAA/Earth System Research Laboratory,R/PSD1, 325 Broadway, DSRC-1D125, Boulder, CO 80305-3337.E-mail: [email protected]

FEBRUARY 2007 W E I C K M A N N A N D B E R R Y 449

DOI: 10.1175/MWR3293.1

MWR3293

Historically, the most well-known extratropicalvariations are baroclinic waves, “blocking,” and zonalindex cycles (e.g., Namias 1954). The latter involvehemispheric variations between blocked and strongzonal flows. In modern times, teleconnection patterns(Wallace and Gutzler 1981, hereafter WG81; Bransta-tor 1992) have been recognized as a general mode ofcirculation variability, of which blocking is a specialcase (Dole 1986, 2007). More recently, zonal mean or“annular” modes of variability are again being high-lighted in diagnostic studies, especially those based onsurface pressure or height (Thompson and Wallace2000). Studies of the evolutionary behavior of zonalmean anomalies have revealed episodes of coherentpropagation all the way from equatorial regions to highpolar latitudes (Feldstein 2001). In the Southern Hemi-sphere, the MJO’s quasi-stationary wave component(Weickmann et al. 1997, hereafter WKS) and a midlati-tude component forced by baroclinic waves (e.g.,Lorenz and Hartmann 2003) likely contribute to suchepisodes.

Although spatial differences are important, thesephenomena all tend to be characterized by 5–10-day-decay time scales (Feldstein 2000) and by large zonalscales. Studies have sought to explain such low-frequency phenomena in terms of multiple equilibria(e.g., Charney and DeVore 1979) or normal modes(Simmons et al. 1983), although current evidence sug-gests that forcing helps determine their time behavior(Newman et al. 1997). Prominent forcing is supplied bythe MJO, topography, the storm tracks, and sea surfacetemperature (SST) variations. A representative compo-nent from this class of red noise processes will make upthe intermediate time scale of the global synoptic–dynamic model (GSDM). We specifically focus on alarge-scale disturbance that develops over the Pacific–North American sector in association with orographi-cally perturbed flow over the eastern Asian and west-ern North American mountains and will refer to thephenomenon as the “�F–�M index cycle.”1 Regionally itincludes teleconnection patterns like the Pacific–NorthAmerican pattern (PNA; WG81). Weickmann (2003,hereafter W03) has studied its synoptic evolution andWeickmann et al. (2000, hereafter WRP) argue that it isthe dominant mode of atmospheric angular momentum

(AAM) exchange and anomaly decay on intermediatesubseasonal time scales.

The fast baroclinic life cycle has been studied forvarious background flows and meridional shears (Sim-mons and Hoskins 1978, 1979, 1980). Disturbancegrowth, phase propagation, energy dispersion, andbreaking are prominent features of such studies(Thorncroft et al. 1993; Whitaker and Sardeshmukh1998) and of the observed atmosphere. Regional baro-clinic wave breaking (Nielsen-Gammon 2001) in par-ticular produces a rapid meridional momentum ex-change that influences even the zonal mean zonal wind.The residual of breaking waves has recently beenlinked with the initiation of teleconnection patterns likethe North Atlantic Oscillation (NAO; Franzke et al.2004). The fast time scale of the GSDM will focus onwave energy dispersion that accompanies baroclinic de-velopments and their interaction with the major moun-tain ranges.

Specifically, synoptic-scale wave energy dispersionwithin the northern and subtropical waveguides overAsia and the Pacific Ocean (Hoskins and Ambrizzi1993; Chang 2005) will represent the model’s fast timescale. The process is linked with 10–30-day oscillationsof the circulation, which have been observed through-out the atmosphere. Wave retrogression at high north-ern latitudes (Branstator 1987), mountain torques overAsia and North America (Lott et al. 2001; Lott andD’Andrea 2005), equatorial convectively coupledRossby and Kelvin waves (Wheeler et al. 2000), andmonsoon oscillations (Hartmann et al. 1992) all displaycoherent behavior on this time scale. This componentcan be energetic for an extended time period as duringthe 1996–97 rainy season over central California (Mo1999). The specific �25-day oscillation represented inthe GSDM involves subtropical flow variations, a likelycandidate for the behavior described by Mo (1999). Mo(2001) has incorporated the intermediate time scale ex-plicitly into the week 1–3 prediction process.

The GSDM organizes these multiple subseasonalphenomena into a repeatable sequence. The relation-ship among the time scales is based on maximizingglobal and zonal AAM anomalies. The GSDM empha-sizes four primary stages but the duration of the cycleand the days between stages are variable. The model isvalid during persistent forcing by sea surface tempera-ture anomalies as well as during the time-varying MJO.In fact, two of the stages represent behavior also ob-served during El Niño and La Niña events. The GSDMis similar to using composites of ENSO or MJO forreal-time monitoring and seasonal or weekly predic-tions, although we seek to explain and account for morevariance through the multiple time-scale approach.

1 A zonal index fluctuation with a broad anomaly center in theTropics (30°N–30°S) and an opposite-signed anomaly at 50°N.The pattern is amplified and extended in time by the meridionaltransports of AAM associated with Rossby wave trains that in-duce a large Northern Hemisphere mountain torque. The zonalwind anomalies eventually decay via the frictional torque.

450 M O N T H L Y W E A T H E R R E V I E W VOLUME 135

A dynamical underpinning for the model is atmo-spheric angular momentum, which is determined by thethree-dimensional distribution of atmospheric zonalwind and mass (Peixoto and Oort 1992). Its global in-tegral is an excellent index of ENSO, the MJO, andother subseasonal variability. Moreover, processes thatchange global AAM, that is, the frictional torque andthe mountain torque, have medium and fast time scales,respectively (WRP). Thus, indices involving these pro-cesses are used to define the components of the GSDM.WRP show that the mountain torque forces AAManomalies and the frictional torque damps them (Eggerand Hoinka 2002), and this will be evident in theGSDM. Atmospheric dynamics linked with wavegrowth and dispersion processes connect the mountainsource regions of AAM anomalies with the subtropicalfrictional sink regions. The latter tend to occur near theseasonally varying zero zonal wind line. The torquesare produced by a variety of known, large-scale pat-terns of wind and pressure as described by WRP andW03.

There are two primary motivations for the synopticmodeling effort. The first is scientific understanding ofthe evolving atmospheric circulation with a practicalgoal of attribution of weather–climate anomalies. Di-agnostic tools and analysis results derived from the sci-ence and research side are used on the monitoring andprediction side to examine cause and effect or the at-tribution of weather climate variations. The applicationof diagnostics to actual forecasting is mostly neglectedin meteorology because of the strong reliance on nu-merical forecast models and lack of a useful synopticframework. The second motivation is daily monitoringof the circulation to evaluate numerical model predic-tions in the subseasonal band, including the potentialpredictability of transitions of the circulation and ofextreme weather events. Extreme events of globalAAM are used as a framework within the GSDM. Thespecific intent is to target the boundary betweenweather and climate, which encompasses the transitionfrom deterministic to probabilistic forecasts. An evalu-ation of numerical forecasts based on synoptic reason-ing is expected to add value because there are well-known, stubborn model errors, particularly in the pre-diction of tropical convection (Lin et al. 2006) and thesubsequent circulation response.

Section 2 introduces aspects of the GSDM with acase study presentation of the 2001–02 northern winterseason. Two rapid transitions of the circulation thatinvolve tropical–extratropical interaction are described,as well as the predictive skill of an ensemble forecastmodel. The derivation of the GSDM is then presentedin section 3. The evolving circulation anomalies of the

different components of the synoptic model are orga-nized using a linear superposition based on the timetendency of global relative AAM. A summary and con-clusions follow in section 4.

2. A case study: December 2001–February 2002

The purpose of this case study is to introduce phe-nomena and variability that will be used to constructthe GSDM. Two transitions of the circulation will beexamined that occur in association with two moderateMJOs. The case begins in a low AAM state typical of aLa Niña circulation regime. A transition then occurs toa high AAM state typical of El Niño, and the case endswith a transition back to a La Niña state. The use of theENSO cycle to describe subseasonal variations of thecirculation and convection emphasizes the strong simi-larity between the responses to tropical convection oninterannual and subseasonal time scales. In fact, stages1 and 3 of the GSDM, which are introduced in the nextsection, closely resemble the well-known La Niña andEl Niño circulation anomalies, respectively. In the fol-lowing, when we will refer to stage 1 and stage 3, thereader should know what we mean. The other out-standing forcing during the case was by the mountaintorque, which represented the other two time scales ofthe GSDM reasonably well. The fast time scale will beobvious but the intermediate time scale is representedbecause regressions on the daily frictional torqueclosely resemble regressions on 5–7-day means of themountain torque (not shown). To focus the study, theroles of the MJO convective signal, the midlatitudemountain torque, and synoptic-scale wave trains aredescribed during two transitions of the large-scale flow.

The MJO activity during 2001–02 not only influencedthe tropical convection and circulation during the studyperiod but also the SST anomalies in the tropical Indo-Pacific Ocean. SST anomalies were recovering from aseries of weak–moderate La Niñas in the previous 3 yrand, during northern fall 2001, positive SST anomalieswere found in the tropical west Pacific Ocean. The firstMJO during November 2001 helped force a shift of theocean warm pool farther eastward toward the date line.This SST change led to a “regime” of �25-day tropicalconvective variability over the west Pacific Ocean—agood example of the behavior described by the �30-day filtered global relative AAM tendency used in theGSDM.

a. Tropical convection

The two MJOs are shown in a time–longitude formatin Fig. 1. MJO 1 forms over the Indian Ocean in Novem-ber 2001, shifts to the west Pacific in early December


2001, and stalls west of the date line. The stalling mayreflect a feedback from the eastward shift of warmocean water cited above. MJO 2 forms over the IndianOcean in mid-January 2002 and reaches the date line inmid-February. It contains more Kelvin and equatorialRossby wave activity than MJO 1 and has its convectivesignal south of the equator for most of February 2002(see Fig. 1). Both MJOs have significant amplitude inthe filtered field, especially at �120°E. Using this lon-gitude as a reference gives a recurrence interval of 65days, which is on the long end of the MJO period range.

To start the process of telescoping to the two transi-tions and their link to MJO-related convective forcing,

seven numbers have been marked on Fig. 1. Thesenumbers “sample” rapid changes within the two MJOs’convective envelope and in the �25-day quasi oscilla-tion along 160°E. They will be referred to as “tropicalconvective flare-ups.” The dates for the flare-ups weredetermined from a time series of the first 2 EOFs of20–100-day filtered outgoing longwave radiation(OLR) anomalies (shown below). The two GSDMtransitions are associated with flare-ups 3 and 5. Here,T1 represents the transition to stage 3 (i.e., like ElNiño) when MJO 1 is located over the west-centralPacific, and T2 is the transition to stage 1 (i.e., like LaNiña) when MJO 2 is over the Indian Ocean. Table 1

FIG. 1. Hovmöller plot (time–longitude section) of OLR anomalies averaged between 7.5°N and 7.5°S, where thecontours illustrate space–time-filtered coherent tropical convection modes for 25 Sep 2001–26 Mar 2002. The bluecontours represent the MJO (solid blue for enhanced convective phase, dashed for suppressed phase). The greencontours are for Kelvin waves and the brown contours isolate an equatorial Rossby mode. See Wheeler and Kiladis(1999) for additional details. MJOs 1 and 2, T1 and T2, and the 1–7 numbering refer to important developmentsdiscussed in the text and listed in Table 1. The lightly shaded horizontal bars highlight the transitions for the casestudy, with T1 (T2) from 19–25 Dec 2001 (12–18 Jan 2002).


Fig 1 live 4/C

gives the calendar dates corresponding to the num-bered events and the two transitions. Although onlyflare-ups 3 and 5 are studied in what follows, the othercases also produced regional and downstream transientimpacts on the atmospheric circulation and on weather-producing disturbances.

b. Midlatitude 250-mb meridional wind

The midlatitude circulation anomalies that accom-pany the tropical OLR signal are depicted using a dailytime-longitude plot. Figure 2 shows the 250-mb meridi-onal wind anomalies averaged between 30° and 60°Nand depicts (i) signatures of storms in the storm-trackregions, (ii) energy dispersion in midlatitude regions,and (iii) slow, quasi oscillations in the midlatitude me-ridional wind pattern. The latter will be discussed interms of the implied geopotential height anomalies,which are marked on the figure. These height patternsinvolve ridging near 150°W (Hs) during the first half ofDecember 2001, troughing in the same location (Ls)during the rest of December into early January 2002,and a return to ridging (Hs) in mid-January–early Feb-ruary 2002. Each persistent episode includes 3–5 syn-optic-scale events whose ridges and troughs tend to de-velop or amplify at the same longitude. The synopticevents have been numbered for each of the three per-sistent “regimes.”

The boundaries of T1 and T2 are marked on Fig. 2and a wave train that extends from 120°E to 90°W ishighlighted during each transition. The wave trains arelinked with the retrogression of existing anomalies (redarrows) and are followed by a series of similar synopticevents. After T2 and the return of ridging to the easternNorth Pacific, the synoptic activity is more spatiallyvariable than during stage 3. It also includes a slow west-ward drift of the circulation anomalies (light dashed

lines) at a time when positive tropical convectionanomalies are over the Indian Ocean and Indonesia.The final synoptic regime seen in Fig. 2 is a progressiveone (light solid lines), which coincides with the returnof convection to the date line around 12 February 2002.

c. Low-frequency indices and their forcing

Figure 3 shows daily indices that capture the low-frequency (�10 day) variations described in Fig. 2 andillustrate the atmospheric response to tropical diabaticheating and orographic forcing to be detailed later. Theindexes include (i) the global integral of AAM, (ii) thefirst EOF of the combined 200-/850-mb vector windfield (with the zonal mean removed), and (iii) the PNAteleconnection pattern. These represent global, hemi-spheric-subtropical, and regional anomaly patterns, re-spectively. All have similar low-frequency behavior,that is, minima in early December 2001 (day 30),maxima in late December–early January 2002 (day 60),and back to minima in late January 2002 (day 80). Thecenter of transitions T1 and T2 are again marked on thecurves. The PNA slightly lags the other curves, which isconsistent with a signal that starts in the Tropics, ex-pands to the subtropics, and eventually affects the re-gional circulation over the midlatitude Pacific Ocean.

The time series of processes that can force thesechanges are depicted in Fig. 4. Figure 4a shows the firstEOF of the zonal mean mountain (red) and frictionaltorque (blue) over the Northern Hemisphere. EOF 1 ofthe mountain torque (not shown) is a monopole patternbetween 20° and 60°N, and EOF 1 of the frictionaltorque (not shown) is a north–south shift in the wintermean boundary of the surface westerly flow. Figure 4bshows coefficients of the first two EOFs of OLR, whichdescribe an eastward movement of the MJO. The con-vective flare-ups numbered in Fig. 1 (see also Table 1)

TABLE 1. Key dates during the case study. Events 1–7 are tropical convective flare-ups while T1 and T2 are circulation transitions.

No. Event

1 6 Nov 2001: persistent eastern Indian Ocean convection from boreal fall 2001 evolves into MJO 12 4 Dec 2001: MJO 1 moves into western Pacific Ocean3 10 Dec 2001: MJO 1 moves to date line and convection then persists for roughly 20 days over relatively warm SSTs

(��0.5°–1.0°C anomalies). Convection is generally suppressed across Indian Ocean during this time4 5 Jan 2002: enhanced convection finally ends west of the date line. A series of convectively coupled equatorial Rossby

waves start to move west from the central Pacific to Africa5 10 Jan 2002: enhanced convection over the Indian Ocean evolves into MJO 26 20 Jan 2002: convection again flares up in the equatorial date line region (�160°E). This area persists for about 10 days

while MJO 2 is farther west and moving east7 10 Feb 2002: enhanced convection develops across the equatorial date line region in association with MJO 2

T1 Transition 1, for 19–25 Dec 2001. The circulation of the atmosphere shifts to GSDM stage 3, a response to enhancedcentral Pacific tropical forcing initiated by flare-up 3 on 10 Dec 2001

T2 Transition 2, from 12–18 Jan 2002. The atmospheric circulation shifts back to GSDM stage 1, a response to the reversalof the tropical convective forcing shown by flare-ups 4 and 5


FIG. 2. Hovmöller plot of 250-mb meridional wind anomalies averaged from 30°–60°N during the period of 1 Dec 2001–28 Feb 2002.The solid horizontal lines depict the periods for T1 and T2, and the “Hs” and “Ls” highlight positions of anomalous synoptic-scale ridgesand troughs, respectively. The red arrows indicate the retrogression of existing anomalies while the light dashed lines show a slowwestward regime shift. The slanted solid black lines indicate progressive circulation anomalies after 1 Feb 2002.


Fig 2 live 4/C

were derived from these OLR EOFs and are alsomarked.

These forcing time series have some distinct low-frequency behavior in addition to the rapid convectionchanges seen in Fig. 4b and the highly variable synopticcomponent seen in the mountain torque time series ofFig. 4a. From Fig. 1, a 65-day recurrence interval forMJO convection was estimated for 120°E; this ismarked at the bottom of Figs. 4a,b. Negative values ofOLR EOF 2 are seen at the endpoints of the interval inthe lower panel and signify that convection is indeedlocated over Indonesia at these times. More generally,OLR EOF 1 (red) leads EOF 2 (blue), consistent withthe eastward propagation of anomalies.

Another low-frequency behavior marked on Fig. 4ais a 50-day recurrence interval in the midlatitude moun-tain torque (Lott et al. 2001). As mentioned previously,the frictional torque (Fig. 4a) acts to damp angular mo-mentum anomalies forced by the mountain torque, but

it is also involved in producing the MJO AAM signal.In the GSDM, the MJO, intermediate �6-day decaytime scale, and 10–30-day oscillation can contribute tocirculation anomalies during stages 1 and 3. These phe-nomena are difficult to disentangle since in all, a posi-tive mountain torque is followed by a negative frictiontorque and vice versa. A section of each time series hasbeen highlighted with a dotted line that shows this lagrelationship for a �50-day oscillation. It is perhapsclearest after T2. Namely, as the large negative moun-tain torque removes westerly momentum from the at-mosphere, easterly wind anomalies and a positive fric-tion torque develop. This slowly removes easterly mo-mentum from the atmosphere, thereby bringing AAMback into temporary balance. It is during this dampingprocess that circulation anomalies of interest to moni-toring and prediction occur, in this case a negativePNA. Another example but with opposite sign is alsohighlighted during December 2001 on Fig. 4a with twoblack arrows.

FIG. 3. Time series plots of indices describing low-frequencyvariations for the period of 1 Nov 2001–28 Feb 2002. The days areon the abscissa, where day 0 is for 1 November, and increasingfrom left to right. The numbers on the ordinate are (top) AAMunits � 1.0 � 1024 kg m2 s�1 and (bottom) dimensionless measuresof amplitude. The (top) is for the global integral of AAM whilethe (bottom) shows the plots for the first EOF of the combined200–850-mb vector wind field (red) and the PNA (blue). Thevertical lines depict the center date for T1 and T2.

FIG. 4. Time series plots for the period of 1 Nov 2001–28 Feb2002 (see Fig. 3). (top) The first EOF of the zonal integral ofthe mountain and frictional torque (red is mountain torque,blue is frictional torque) and (bottom) the first 2 EOFs of 20–100-day filtered OLR (red is EOF 1, blue is EOF 2). The text on theright indicates the location of anomalous convection correspond-ing to positive and negative values of each EOF. The IndianOcean is represented by IO. Shaded vertical bars represent T1and T2.


Fig 3 4 live 4/C

The locations of T1 and T2 are marked with shadingon Fig. 4. The transitions follow closely the very largepositive and negative maxima in the mountain torqueanomaly, which are embedded in strong daily variabil-ity as synoptic systems move over the topography.Asian–European topography is a strong contributor toboth the positive and negative anomaly while NorthAmerican topography contributes primarily to the laternegative anomaly (not shown). The mountain torqueevents are linked with the amplification of a baroclinicwave downstream of the Asian topography over thewestern half of the North Pacific. During T1, the am-plifying wave leads to a cyclonic wave break over theeast Pacific that brings westerlies south and ushers instage 3. The opposite happens during the transition tostage 1.

Figure 4b shows that the transitions occur 5–10 daysafter flare-up 3 and 1–3 days after flare-up 5. This sug-gests a loose relationship between rapid transitions inthe circulation and the sudden shift of convectionwithin the MJO convective envelope. In this case, it isthe midlatitude mountain torque that is more directlylinked with both transitions. However, the persistenceof tropical forcing, as represented by the heavy hori-zontal bars on the EOF 1 OLR time series, undoubt-edly contributed to the persistence of the resultinglarge-scale circulation anomalies.

d. Synoptic maps during circulation transitions

Figure 5 shows selected daily maps of the 150-mbvector wind anomaly during T1. The key anomaliesfrom an MJO perspective are suppressed convectionover the Indian Ocean and active convection near thedate line (not shown, but see Fig. 1). Early in the se-quence (Figs. 5a,b), a wave train is evident across theIndian Ocean/south Asia with a trough near 20°N,70°E. The trough is quasi-stationary and eventuallyevolves into a large cyclonic anomaly covering the en-tire region (Fig. 5f). The MJO at this stage helps forcethe trough and sets the phase of a wavenumber 5–6wave train through which energy flows eastward. An-other more stationary wave train farther north (60°N)combines with the subtropical wave train over the mid-latitude North Pacific in Fig. 5b, which precedes thewave amplification over the west Pacific seen in Figs.5d–f. The phase of the amplifying couplet west of thedate line is consistent with the orographic response to apositive mountain torque (W03). Baroclinic processesand upper-level outflow from the tropical convectionwest of the date line help the amplification process. InFig. 5f, the downstream low over the northeast Pacifichas developed a negative tilt, and a full cyclonic break-

ing event is in progress. This behavior also becomeslinked with a retrograding anticyclonic anomaly acrossCanada and the North Atlantic, which allowed for astrong projection onto the positive phase of the PNAand the negative phase of the NAO. This pattern ofstrong tropical–subtropical westerlies stays in place for�15 days.

Almost the opposite behavior was observed duringT2, whose synoptic evolution to GSDM stage 1 isshown in Fig. 6. Now instead of a trough, there is a ridgeat 20°N, 70°E (Figs. 6a,b), which is being forced by thestrong convection over the Indian Ocean. The phase ofthe wave train is reversed compared to Fig. 5, and theIndian Ocean ridge grows into a large anticyclonicanomaly over south Asia as the transition matures (seeFig. 6f). The downstream amplification over the westNorth Pacific also occurs, but with the phase reversed(Figs. 6b–d) and little evidence of a preexisting wavetrain farther north. This leads to a wave break over theeast Pacific (Figs. 6e,f) that becomes anticyclonic alongthe U.S. west coast. The stage 1 pattern was maintainedby additional meridional–zonal flow variations leadingto more anticyclonic wave breaking along the U.S. westcoast (not shown). The final wave break occurred dur-ing late January 2002 and linked up with an anoma-lously strong subtropical jet, forced by tropical convec-tive flare-up 6 near the date line, to produce an extremewinter weather event (snow and freezing rain) over theGreat Plains. The GSDM stage 1 characteristics of thecirculation finally broke down in mid-February 2002(see Fig. 2).

e. Predictive skill of circulation transitions

The abrupt onset of the stage 3 and stage 1 circula-tion regimes has forecast implications for the mediumrange. Figure 7 shows the ensemble mean forecast skillout to day 15 during the 2001–02 winter season using a1997 version of the National Centers for EnvironmentalPrediction (NCEP) Medium-Range Forecast model.This model has a 25-yr reforecast dataset available andreal-time predictions are posted on the Web (Hamill etal. 2004; see http:www.cdc.noaa.gov/people/jeffrey.s.whitaker/refcst/week2/). The skill measure used here isthe spatial correlation between verifications and pre-dictions of Northern Hemisphere 150-mb streamfunc-tion anomalies. There are 3 periods where the 11-dayensemble-mean forecast skill of the Northern Hemi-sphere 150-mb streamfunction anomaly is relativelypoor (�0.5). The common thread in these low-skill re-gimes is that a major change in tropical convective forc-ing is observed (and presumably not captured) duringthe forecast cycle. The major convective changesare highlighted with arrows in the top panel of Fig. 7


FIG. 5. The daily evolution of 150-mb vector wind anomalies for T1, the transition to stage3 of the GSDM. Here, Hs and Ls refer to anomalous anticyclonic and cyclonic circulations. Thedates are (a)–(f) 19, 20, 21, 22, 23, and 25 December, respectively. The vertical lines highlight90°E, 180°, and 90°W.


Fig 5 live 4/C

FIG. 6. Same as in Fig. 5 but for T2, the transition to stage 1 of the GSDM. The dates are(a)–(f) 12, 13, 14, 15, 16, and 18 January, respectively.


Fig 6 live 4/C

(i.e., flare-ups 3, 5, and 7). Note that the 5 and 7 tran-sitions occur near the end of the forecast cycle, implyinga rapid impact on the circulation anomalies of theNorthern Hemisphere, if indeed they are the cause forthe low forecast skill.

For T1 and T2, the amplification of a wave distur-bance over the western North Pacific is a key synopticevent. On 23–24 December 2001, the “low–high” cou-plet west of the date line (Fig. 5d) was predicted 11 daysin advance but the “high–low” couplet in the sameplace on 15–16 January (Fig. 6d) was not. A clue aboutwhat may be happening is derived from the generalpattern of forecast skill described above for the 2001–02winter. The forecast for 23–24 December 2001 is initial-ized after flare-up 3 while the forecast for 15–16 Janu-

ary 2002 is initialized before event 5. Failure to capturethe start of flare-up 5 and the large negative mountaintorque in the forecast cycle presumably contributed tothe low forecast skill during the second transition.Many more cases need to be examined to confirm theseassertions.

f. Discussion

Several atmospheric phenomena and processes wereintroduced during the case study description. Tropicalconvective forcing involved multiple time scales includ-ing the 30–60-day MJO, 20–30-day convective flare-ups,and other convectively coupled equatorial waves. To-pographic forcing from synoptic-scale disturbances wasclustered on a 50-day time interval and produced zonalmomentum anomalies that were removed by the fric-tional torque. The PNA teleconnection pattern was in-volved in the removal process. Finally, the phase ofsynoptic-scale wave trains over the Asian–Pacific sectorwas related to tropical convective forcing over theIndo-Pacific warm pool region and to subsequent anti-cyclonic and cyclonic wave breaking over the easternNorth Pacific.

The 50-day “oscillation” in the mountain torque isconsistent with the 6-day decay time scale of the �F–�M

index cycle. A red noise process with a 6-day decaytime has its variance concentrated in a band with peri-ods at around 6 days � 2 � �38 days. Plotting itsspectrum with the log of frequency as the abscissa in avariance-conserving format shows this feature of rednoise most clearly (see, e.g., Fig. 2 of WRP). A 50-dayoscillation is a representative example from such a pro-cess, but of course no coherent forcing exists at 50 daysor any other period in the red noise background.

In the case study, these and other processes are seenas working together to produce the evolving atmo-spheric circulation anomalies. The indices in Fig. 3show a slow evolution while Fig. 2 has the transitionoccurring rapidly in association with synoptic-scalewave trains. The latter are seen as a mechanism for thespatial spreading of information about the changes inforcing from key regions around the hemisphere (e.g.,western ocean baroclinic zones, tropical convectivezones, and centers of low-frequency variability). Cer-tainly, a fortuitous or random nature must be assumedabout these fast (�30 m s�1) eastward-moving distur-bances and their role in the transitions of the circula-tion; that is, there is always another synoptic system orwave train that can play the transition role. After thetransition, repeatable synoptic events were superim-posed on the quasi-stationary flow, and these representthe opportunities for skillful extended forecasts of syn-optic-scale behavior.

FIG. 7. (top) Time series plots of OLR EOFs 1 and 2 (as in Fig.4) and (bottom) forecast skill for a forecast model ensemble meanduring the period of 1 Dec 2001–28 Feb 2002 (abscissa, days in-creasing from left to right). Here, “IC,” “V,” and the vertical lineshighlight the model initial condition and verification times for thethree cases discussed in the text. Forecast skill is expressed interms of the anomaly correlation coefficient over the entireNorthern Hemisphere of 150-mb streamfunction. The contour in-terval on the (bottom) is 0.3 and the black dots show the dates ofthe lowest day 11 forecast skill. The slanted lines indicate themodel forecast cycle (day 1–15 lead) for three cases, including T1and T2. The horizontal line highlights the day 11 lead.


Fig 7 live 4/C

The basic perspective is that forcing is of primaryimportance for determining the evolution of the atmo-spheric circulation and that different sources of forcingproduce circulation responses that combine linearly toproduce the circulation anomalies at any particulartime. Anomalies may be maintained by feedbacks buteventually they disperse as the forcing waxes andwanes, even when coupling from persistent SST anoma-lies is involved. This perspective is supported bySardeshmukh et al. (1997), Newman and Sardeshmukh(1998), and Newman et al. (1997), who demonstrate theimportance of forcing for the evolution of low-fre-quency circulation anomalies. The success of the Wink-ler et al. (2001, hereafter WNS) linear inverse model(LIM) of weekly circulation anomalies is based on theimportance of tropical and other forcing as a source forweek 1–3 predictive skill.

WNS’s linear inverse model of 7-day averages hasfeatures in common with the GSDM introduced in thenext section. The LIM has three optimal structures thatundergo nonmodal growth over a wide range of trun-cations and maximized growth rates. Two optimals arelinked with forcing from the MJO and ENSO while thethird is a PNA pattern linked to eddy feedbacks inmidlatitudes. The LIM is objective, so it can be used fordynamical feedback studies (WNS) as well as predict-ability studies (Newman et al. 2003).

The GSDM is subjective but includes a synoptic com-ponent and a submonthly oscillation in addition to theMJO and the PNA, arguably four “modes” versus threefor LIM. Its dynamics are based on the terms in theglobal and zonal AAM budget. Meridional and verticaltransports help produce the torques at the surface. Alinear phasing of GSDM components is assumed, andthis unites several time and space scales within themodel. The model does not explicitly include ENSO,but knowledge of the ENSO cycle is critical when ap-plying it in real time. Both models can be further ex-tended and are tools for monitoring, attribution, andprediction. The GSDM is introduced next.

3. A Global Synoptic–Dynamic Model (GSDM) ofsubseasonal variability

The synoptic model organizes four subseasonal timescales into a single picture that describes a recurringevolution of global and regional weather climate pat-terns. Numerous indices could have been chosen to de-fine a representative spatial evolution for each timescale. We use (i) the first EOF of 20–100-day filteredOLR to represent the MJO, (ii) the daily global fric-tional torque with the MJO linearly removed to repre-sent the “�F–�M index cycle” (W03), and (iii) the �30-

day filtered relative AAM tendency to represent waveenergy dispersion over the mountains (W03) and 10–30-day oscillations. The indices are computed for thesixteen winter segments, November–March 1979–95.The segment mean is removed prior to the regressionanalysis to minimize contributions from interannualvariability. Resulting anomalies will be interpretedrelative to a smoothed seasonal cycle.

Figure 8 shows the three indices. Their different timebehavior is self-evident and ranges from quasi-oscil-

FIG. 8. Indices for 16 winter segments from November–March1979–95. (top) The first EOF of 20–100-day filtered OLR repre-sents the MJO, (middle) the daily global frictional torque with theMJO linearly removed represents teleconnection patterns, and(bottom) the �30-day filtered global relative AAM tendency rep-resents wave energy dispersion over the mountains. The abscissasare time expressed as days while the ordinates are nondimen-sional measures of amplitude.


Fig 8 live 4/C

latory (Fig. 8a) to red noise (Fig. 8b) to white noise plusa �20–25-day oscillation (Fig. 8c).2 We implicitly as-sume that these time scales are adequate to account forsome interesting variations in the subseasonal band,with a focus over the Tropics, Asia, and the Pacific–North American region. First, however, we examinethe relationship to global and zonal mean AAM, whichare used to “phase” the model components.

a. Atmospheric angular momentum

In the case study, global AAM (Fig. 3) undergoes arelatively smooth evolution despite the complicatedforcing depicted in Fig. 4. A careful examination of theAAM time series can discern the responses to the fastand medium excursions of the global mountain and fric-tional torques seen in Fig. 4, while the overall �60-dayoscillation implies a forcing by the weaker but morepersistent torques associated with the MJO. Differenttime scales are clearly working together to produce theobserved behavior. We now illustrate these buildingblocks and suggest why and how they may be related.

Figures 9b–d show the global and zonal AAManomalies obtained when regressing onto the three in-dices of the GSDM in Figs. 8a–c. The heavy solid lineson Figs. 9a–e confirm that all three indices have a globalAAM signal. The lag at which the AAM anomalycrosses 0 is ��2 days (Fig. 9b), �7 days (Fig. 9c), and0 days (Fig. 9d) for the 3 GSDM components. This isthe key assumption made in constructing our model.3

The point is that a linear combination of the three timescales, when shifted by these amounts, would result in alarge relative AAM time tendency. We are specificallyinterested in large anomalies because synoptic experi-ence indicates that extreme events consist of multipletime scales “working together.” Such a linear combina-tion would produce torques whose sum resembles thetime series seen in Fig. 4a of the case study. MaximumAAM tendency would occur at stage 2 of the GSDMand would have contributions from all model compo-nents.

The zonal mean AAM anomalies when added depicta coherent signal of AAM anomalies moving out ofequatorial regions toward the subtropics (Fig. 9a) and aweaker signal of anomalies moving equatorwardaround 50°N. The intermediate time scale �F–�M indexcycle (W03) imposes an asymmetry around day 0. Mo-

mentum transports by different types of eddies (e.g.,subtropical wavenumber 1, midlatitude teleconnec-tions, and midlatitude synoptic transients) play an im-portant role in forcing all three of the zonal meananomaly fields and provide a dynamical link betweenthe time scales.

In the next subsection, the synoptic patterns relatedto the global and zonal AAM changes seen in Fig. 9 arepresented. Since the �30-day tendency and the fric-tional torque regressions are performed on global indi-ces, the results will emphasize those patterns that con-tribute to global AAM changes. For the �30-day ten-dency, the three main topographic regions arerepresented while for the global frictional torque, theNorthern Hemisphere surface wind over both oceanbasins will be important. During individual cases ofsubseasonal variation, not all regions will always con-tribute to the forcing. For example, in the case study,Asia was the primary contributor to the positive moun-tain torque before T1 while Asia and North Americaboth contributed to the negative torque before T2.Nonetheless, a simultaneous forcing from the three re-gions is not unusual and can be organized by the pole-ward propagation of zonal mean wind anomalies or bythe dispersion of Rossby waves into each hemispherefrom west Pacific tropical heating. In general, however,the phasing of regional patterns is influenced by the useof a global measure on which to base the analysis andcan distort important regional behavior.

b. Lagged regression sequences

Lagged linear regressions of global, 2D fields ontoeach index are used to define an evolution of circula-tion anomalies and will be referred to as a lagged re-gression sequence. Figures 10–12 show sequences 1–3of 200-mb vector wind and sea level pressure (SLP)anomalies when regressed onto the 3 indices of Fig. 8.The duration and time interval of each sequence em-phasize its time scale. Sequence 1 is 40 days long with a10-day interval, sequence 2 is 18 days long with a 4-dayinterval, and sequence 3 is 8 days long with a 2-dayinterval. Global fields are shown because real-timemonitoring suggests that coherent subseasonal interac-tions occur across broad latitudinal bands, often cen-tered on either side of the equator. The sequences il-lustrate the well-known observation that large spatialscales coincide with long time scales. Beyond this, thereare other features familiar to weather and climate sci-entists.

In sequence 1 (Fig. 10), the subtropical cyclones/anticyclones of the MJO are seen as they slowly propa-gate eastward from day �20 through day 0 to day 20. Atday 0 (Fig. 10), convection is active over the equatorial

2 A statistically significant �25-day oscillation appears in thespectra of global relative AAM in 2 different 16-winter periods:1962–78 and 1979–95.

3 One could also use the time of maximum zonal AAM ten-dency at the equator and get slightly different numbers.


western Pacific and global AAM has a large positivetime tendency, at which time equatorial westerlies arealready present over the Western Hemisphere. In se-quence 2 (Fig. 11), a negative Pacific–North Americanteleconnection pattern (W03) develops by day �2 asRossby waves disperse across Asia and then NorthAmerica during the 18-day sequence; this contributesto a large positive frictional torque anomaly at day 0(not shown). In sequence 3 (Fig. 12), rapid energy dis-persion events (30 m s�1) are seen centered over theEast Asian, North American, and South Americanmountains at day 0 and contribute to a positive globalmountain torque anomaly. The events are embedded ina pattern of wavenumber 0–2 zonal wind anomalies,some of which are highlighted by arrows. Four daysafter the positive torque, westerly flow anomalies ex-tend from the equatorial east Pacific eastward and pole-ward to the midlatitude central Pacific. These anoma-lies represent the �20-day quasi-oscillatory componentof the GSDM (see also Fig. 9d).

Interestingly, sequences 1–3 all have local statisticallysignificant wind and SLP anomalies in tropical regions,even the two faster modes of variability. The featuresare characterized by wavenumber 0–1 zonal windanomalies at upper levels and provide a synoptic pat-tern that links the different types of subseasonal vari-ability. This complements and extends the results forthe global and zonal AAM relationship that is the basisfor the model.

c. The synoptic–dynamic model (GSDM)

Figure 13 shows the 4 stages of the GSDM nominallycentered about 12 days apart with an �50-day oscilla-tion due to the MJO. These numbers have a wide rangesince the subseasonal band is broad, and transition be-tween phases can occur rapidly. A complete temporalevolution of anomalies is shown only for the MJO.Twenty-two maps representing 11 lags for both OLREOF 1 and EOF 2 were examined and the 4 lags in Fig.13 were chosen to represent the MJO. The EOFs are inquadrature and show similar patterns when shifted by�10 days. Table 2 shows the correspondence between

the stages and the lags for the two EOFs. The Hs and Lsfor the other components are placed with a specificstage based on the “large AAM tendency” criteriondiscussed in relation to Fig. 9. Specifically, the coloredHs and Ls shown on sequences 2 (Fig. 11) and 3 (Fig.12) are used to complete the construction of the stages.

1) STAGE 1

This stage represents a particular phasing of the MJOand the �F–�M index cycle of the model. Stage 1 andstage 3 are considered the more persistent stages of theGSDM. During stage 1, the anomalous anticycloneslinked with the MJO cover most of the tropical EasternHemisphere with downstream cyclones over the sub-tropical west Pacific Ocean. Tropical convectionanomalies are consolidated over the eastern IndianOcean as the MJO convective forcing has intensifiedfrom stage 4. In the subtropics, easterly flow anomaliescover the west Pacific and also weakly cover the Atlan-tic Ocean. The anomalies represent an amplification ofthe wintertime climatological stationary waves in theTropics and subtropics (see Fig. 9a of WKS), althoughthe Pacific jet is retracted.

The brown Hs and Ls over the Northern Hemisphererepresent the �F–�M index cycle. A negative PNA pat-tern is a prominent feature of the wave train distur-bance. The circulation centers of this stochastic modeapproximately phase with some of the circulationanomalies associated with the MJO. Together, easterlyzonal wind anomalies in subtropical latitudes of theWestern Hemisphere and in the Tropics of the EasternHemisphere lead to the very low relative AAM. Asthese easterly flow anomalies reach the surface, theylead to a positive frictional torque, which sets the stagefor an increase in AAM and a possible transition tostage 2.

Although not depicted in Fig. 9, the general anoma-lous pattern of synoptic variability is similar to whatoccurs during La Niña. It involves a northward-shiftedstorm track and enhanced wave energy propagatinginto the Tropics. Matthews and Kiladis (1999) showthat during this phase of the MJO, the Pacific

←

FIG. 9. The total global atmospheric angular momentum (solid curve), the global mountain torque (long dash curve), and the globalfrictional torque (short dash curve) anomalies obtained by lag regressions onto various indices using 16 northern winter seasons(November–March 1979–95). The left ordinate labels are Hadleys (1 Hadley � 1.0 � 1018 kg m2 s�2) and the right labels are AAM units(1 unit � 1.0 � 1024 kg m2 s�1). The abscissa is lag where negative (positive) values mean the regressed quantity leads (lags) the index.For the contours, the right labels also represent latitude/10 (i.e., 6 � 60°N, etc.). The contour and shading interval is 0.1 � 1024 kg m2

s�1 (the value corresponds to a vertical and zonal mean zonal wind anomaly of 0.3 m s�1 at 30°N). The indices used are (a) the dailyglobal AAM tendency, (b) the first EOF of 20–100-day filtered OLR, (c) the global frictional torque minus the MJO, (d) the globalrelative AAM filtered to retain �30-day periods, and (e) the global mountain torque. The contours start at 0.05 � 1024 kg m2 s�1 in (d).


FIG. 10. The 200-mb vector wind (arrows) and SLP anomalies (shading) obtained by lagregression onto EOF 1 of 20–100-day filtered OLR shown in Fig. 8 (top; sequence 1). For theSLP anomalies, stippling (hatched) represents anomalously high (low) pressure. The Hs andLs depict anticyclonic (cyclonic) 200-mb vector wind anomalies. Only wind anomalies locallysignificant at 95% are plotted. The red and blue Hs and Ls approximately correspond to thelight gray Hs and Ls in Fig. 13 (see also Table 2).


Fig 10 live 4/C

FIG. 11. Same as in Fig. 10 but regressed onto the daily global frictional torque shown inFig. 8 (middle; sequence 2). The brown Hs and Ls are placed on Fig. 13 as part of stage 1and stage 3 (opposite phase) of the GSDM.


Fig 11 live 4/C

FIG. 12. Same as in Fig. 10 but lag regressions on the �30-day filtered, global relativeAAM tendency index given on Fig. 8 (bottom; sequence 3). The green Hs and Ls are placedon Fig. 13 as part of stage 2 and stage 4 (opposite phase) of the GSDM.


Fig 12 live 4/C

FIG. 13. The four stages of the GSDM of subseasonal variability for the Northern Hemisphere cold season (November–March). Thered (blue) isopleths and shading depict subtropical anticyclonic (cyclonic) 200-mb streamfunction anomalies (interhemispheric signreversal is understood) that accompany MJO tropical convection anomalies as they move east. The black (hatched) shading shows theareas of enhanced (suppressed) convection with the MJO. The Hs and Ls are used to show the associated anomalous anticyclonic (orhigh pressure) and cyclonic (or low pressure) gyres. The lighter gray Hs and Ls are for the MJO while the heavier gray ones illustratea west Pacific wave train linked to the MJO at stage 2. The brown Hs and Ls depict teleconnection patterns associated with the frictionaltorque and the green ones show synoptic-scale wave trains.


Fig 13 live 4/C

waveguide tends to be “leakier” since the jet stream isweaker and westerly winds extend over a broad latitu-dinal band. As wave energy disperses southeastwardinto the east Pacific ITCZ, the resulting convectionanomalies (Kiladis and Weickmann 1997; Matthewsand Kiladis 1999) can lead to subtropical jets that com-bine with the western United States trough and pro-duce baroclinic developments over the Great Plains.

Stage 1 can be characterized by an �weekly variationbetween strong meridional flow anomalies and strongzonal flow anomalies during northern winter. Transi-tions from meridional to zonal flows occur in associa-tion with baroclinic waves that tend to break anticy-clonically over the east Pacific Ocean. Broadly speak-ing, stage 1 represents a “La Niña” basic state, whichhas been shown to support greater intraseasonal vari-ance over the North Pacific Ocean (Compo et al. 2001)and life cycle 1 (LC1; anticyclonic) of baroclinic waveactivity (Shapiro et al. 2001).

2) STAGE 2

Stage 2 represents a transitional phase of the GSDMwhere the MJO moves into the Pacific Ocean regionand synoptic-scale energy dispersion contributes tostrong positive mountain torques. Positive MJO con-vection anomalies that were previously centered westof 120°E now set up over the western Pacific at around150°E. Weickmann and Khalsa (1990) have shown thatthis transition can occur rapidly in association withhigh-frequency tropical transients since identified asconvectively coupled equatorial Kelvin waves byWheeler and Kiladis (1999). The MJO circulationanomalies are also transitional as twin anticyclonesmove into the western Pacific and twin cyclones coverthe remainder of the Tropics including the western In-dian Ocean. The anomaly pattern represents an east-ward shift of the climatological flow in the Tropics andsubtropics (see Fig. 9b of WKS).

The green Hs and Ls are the fast time-scale patternsthat give a large positive mountain torque and precede

stronger westerly flow in the subtropics from 10–30-dayoscillations. In the Northern Hemisphere, two wavetrains over Asia meet over the west Pacific and dispersedownstream. In the Southern Hemisphere, wave trainsare shown that produce positive mountain torques overthe South American Andes and the African highlands.

Stage 2 often represents a sudden transition to newtropical heat sources, and considerable transientRossby wave activity emanates from the new sourcesover the east Indian and the west Pacific Oceans. Overthe west Pacific Ocean, this is characterized by thespinup of upper-level anticyclones, whose circulationthen interacts with midlatitude weather systems. Onesuch interaction can initiate a growing Pacific Oceanwave train (the heavy gray Hs and Ls) that extendsdownstream across North America. Although the wavetrain is depicted in stage 2, it is best developed 6–10days after convection moves into the western PacificOcean region. In that case, the green Hs and Ls areprecursors to the dark gray Hs and Ls.

WNS obtain a similar wave train in their study of theresponse to tropical heating. The initial state of theirsingular vector 2 (SV2) would project onto both theconvection and green circulation centers shown at stage2. The gray Hs and Ls emanating from the tropical westPacific Ocean region represent the final state of SV2.Other studies of MJO composite circulation anomalies(e.g., Knutson and Weickmann 1987) find a similar fea-ture. The wave train is seldom a simple Rossby wavedispersing from a tropical heat source (Hoskins andKaroly 1981; Sardeshmukh and Hoskins 1988) but of-ten involves tropical–extratropical interaction on fasttime scales.

3) STAGE 3

As the GSDM convection anomaly moves eastward,the circulation anomalies now act to weaken the normalwintertime climatological flow in the Tropics and sub-tropics (see Fig. 9c of WKS), but at the same time ex-tend and strengthen the jet across the Pacific Ocean.The brown Hs and Ls connecting Asia and NorthAmerica now project on a positive PNA. Strong west-erly flow occurs at 35°N over the Western Hemisphereand in the Tropics over the Eastern Hemisphere, fromthe combination of the MJO and the intermediate time-scale �F –�M index cycle. The storm track is farthersouth over the Pacific and can give rise to extreme rain-fall events along the West Coast. Cyclonic wave break-ing is often observed over the east Pacific Ocean, up-stream of North America. Stage 3 represents an “ElNiño” basic state, and while the patterns are opposite tostage 1, the synoptic variability tends to be less extremeduring stage 3.

TABLE 2. GSDM stages and their relation to OLR EOF 1 andEOF 2. The “OLR EOF and lag” column contains the EOFs andlags that make up the MJO contribution to the four stages, asdepicted in Fig. 13. None of these are shown explicitly in Fig. 10,which shows regressions onto EOF1 only.

StageOLR EOF

and lagLag of other

EOF Fig. 10 shows

1 EOF 1, day �15 EOF 2, day 0 Neither2 EOF 2, day �10 EOF 1, day 0 c: EOF 1, day 03 EOF 2, day 0 EOF 1, day �10 d: EOF 1, day �104 EOF 2 day �10 EOF 1, day �20 e: EOF 1, day �20


4) STAGE 4

Stage 4 is similar to stage 2 but with opposite sign andslightly earlier in the MJO life cycle. For example, sup-pressed convection still covers western Indonesia instage 4 whereas enhanced convection is farther east atstage 2. The MJO circulation anomalies now produce awestward shift of the wintertime climatological flow inthe Tropics and subtropics. Over the Indian Ocean, thestrong subtropical cyclones of stage 3 are transitioningto anticyclones as convection redevelops over the cen-tral Indian Ocean. This stage has three centers of MJOconvection: east of the date line, over South America,and over Africa/west Indian Ocean.

On the synoptic time scale, stage 4 is represented bythe sequence of green Ls and Hs, the opposite phase tostage 2. The phase of the south Asian wave train is setby the Indian Ocean convection anomaly located southand east of the anomalous anticyclone at around 60°E.This wave train phases with a separate wave train in thenorth Asian waveguide (which produces a negativemountain torque there) and then together they disperseeast and amplify across the North Pacific toward NorthAmerica. The combination of a negative mountain andfrictional torque from the MJO and a negative moun-tain torque from the synoptic-scale dispersion leads to astrong negative AAM tendency and sets the stage fordecreasing westerly flow in the atmosphere.

d. The combined AAM cycle

Much is known about the subseasonal budget ofglobal and zonal AAM based on recent diagnostic stud-ies using reanalysis data. For the global budget, Weick-mann et al. (2000) and Egger and Hoinka (2002) showthat the mountain torques force AAM anomalies andthe frictional torque damps them. In the semantics ofFourier analysis, this means the friction torque leadsthe mountain torque. All subseasonal variability hasthis characteristic. The zonal budget brings in the roleof AAM transports, which are zero in a global integral.Meridional transports provide a link back to the struc-ture and orientation of troughs and ridges within thespatial patterns shown in Fig. 13. Subseasonal zonalAAM anomalies have well-developed poleward (Feld-stein 2001) and downward propagation that extendsfrom the equatorial tropopause to the subtropical solidearth (Egger and Weickmann 2007; Egger and Hoinka2005). Dynamically, many questions remain about thecontribution from different mechanisms in this process.For example, Moncrieff (2004) proposes a role for thevertical transport of zonal momentum due to the struc-ture of organized mesoscale convective complexes. Un-fortunately, the zonal AAM budget cannot provide

even rudimentary answers because it is not balanced ineither the NCEP–National Center for Atmospheric Re-search (NCAR) (WKS) nor the European Centre forMedium-Range Weather Forecasts (ECMWF) reanaly-ses (Egger and Hoinka 2005). The zonal mean flux con-vergence of relative AAM is large compared to the sumof zonal mean torques, even when the Coriolis andgravity wave drag torques are included. This contrib-utes to a systematic dipole error in the zonal AAMbudget as shown by W03 (see his Figs. 3c,d).

In this section, we are not so much interested in theAAM budget as in using it to bring out additional fea-tures of the GSDM and to relate its spatial patterns inFig. 13 with the combined AAM cycle. Some of thefeatures of the cycle are summarized in Table 3. Figure14 shows the lag regression of the global and zonalAAM, the flux convergence of AAM, and the moun-tain and frictional torque onto daily time series of theglobal relative AAM tendency for November–March1979–95. The approximate locations of the GSDMstages are shown at the bottom of the figure.

In Fig. 13, the Hs and Ls from different time scaleswere placed on the four stages without considering theactual time behavior that might ensue. Figure 14 showsthis in an average sense for the global and zonal meanfields by regressing on an index that contains all thecomponents of the GSDM (i.e., the daily global relativeAAM tendency). The time behavior is clearly asym-metric with respect to zero lag, as would be expected, ifonly because of the intermediate time scale �F–�M indexcycle. There appears to be a buildup phase during stage1 (see Fig. 14 prior to day �5) where several processesare persistent, and there is a gradual decrease (in-crease) in relative AAM (frictional torque) anomalydue to a negative mountain torque. This occurs early inthe MJO’s life cycle when positive convection anoma-lies are over the Indian Ocean and the intermediatetime scale contributes a negative PNA as positive fric-tional torques increase (Fig. 14c).

There then appears an abrupt reversal or weakeningin all anomalies around day �2, arguably led by a re-versal in the meridional AAM transport across 30°N,from poleward before to equatorward after. This occursjust as the zonal mean easterly flow anomalies in thesubtropics reach their peak values at 25°N. At the sametime, the dominate wave train in the GSDM shifts fromthe intermediate time-scale teleconnection type (stage1) to the wave-packet-dominated fast time-scale type(stage 2). The latter helps reverse the mountain torqueand possibly initiates the “flip” in meridional trans-ports. Figure 14b has a momentum source due to trans-ports that extends from the northern to southern sub-


tropics. The MJO is also undergoing a transition at thistime when tropical convection moves out of the IndianOcean and into the west Pacific Ocean region. A fur-ther forcing of the torques by the MJO could then leadto a continued oscillation. Figure 14a shows moredamped anomalies after day 0 again reflecting the �F–�M index cycle.

During an oscillation, the vertically integrated AAManomaly (Fig. 14a) alternates between easterly andwesterly flow anomalies that propagate from equatorialregions to the subtropics. The oscillation represents theMJO along with a sharpening of the curve by 10–30-dayvariations. Global angular momentum is at a minimumat stage 1 when negative AAM anomalies (easterlywind anomalies) are moving off the equator and tropi-cal sea level pressure is low. By stage 2, the easterlyanomalies are approaching the subtropics and weaken-ing on the equator. Tropical SLP is on the rise and MJOconvection is active over the western Pacific. By stage 3,westerly flow anomalies are lifting off the equator,

tropical SLP is high, and global AAM reaches a maxi-mum. Convection is near the date line, but it is stronglysuppressed over the Indian Ocean from both the MJOand 10–30-day oscillations. The cycle ends with stage 4as westerly wind anomalies move off the equator andconvection is active in the three separate centers.

The frictional torque tends to be large during stages1/2 and 3, when anomalies are more persistent thanduring stages 2 and 4. Synoptically, stage 1 is repre-sented by strong trade winds and a northward-shiftedwesterly flow, especially over the Atlantic and PacificOceans. Sometimes, blocking can contribute to thetorque through easterly flow anomalies that are largeand farther north. The mountain torque tends to belarge during stages 2 and 4, which also tend to be moretransient with faster time scales involved. The positivemountain torque in the Southern Hemisphere is due tothe Andes and develops as convection shifts into thewestern Pacific between stages 1 and 2 (Madden andJulian 1972; Milliff and Madden 1996). In the Northern

TABLE 3. Summary of the GSDM stages.

Characteristics

Stage 1 MJO convection around 110°E with enhanced (suppressed) tropical convective forcing across the eastern (western)hemisphere

Amplified (tropical/subtropical) seasonal base stateLow AAM/strengthened subtropical momentum sinkPNA � 0 forced by �F–�M index cycle (�M � 0, �F � 0 sequence)Contracted East Asian and North American jets, displaced poleward/split flows over the oceansThe MJO and �F–�M index cycle give large positive frictional torquesLa Niña–like base state with Pacific Ocean anticyclonic wave breakingWave energy dispersion favors high-impact weather across the U.S. plains

Stage 2 MJO convection around 150°EEastward-shifted seasonal base stated(AAM)/dt �0 and momentum sink shifting polewardThe MJO and fast time-scale component give large positive mountain torquesWestern Pacific–North American Rossby wave train; strong ridge from U.S. West Coast into AlaskaAsian–Pacific wave train favors east Pacific cyclonic wave break for transition to stage 3Much below normal temperatures possible across central and eastern United States

Stage 3 MJO convection around date line with enhanced (suppressed) tropical convective signal across the western (eastern)hemisphere

Deamplified seasonal base stateHigh AAM/weakened subtropical momentum sinkPNA � 0 forced by mountain torque � 0, friction torque � 0 sequenceExtended East Asian and North American jets, displaced equatorward/split flows across the continentsThe MJO and �F-�M index cycle give large negative frictional torquesEl Niño–like base state with east Pacific Ocean cyclonic wave breakingHigh-impact weather event possible along the West Coast

Stage 4 MJO convective signal across the Western Hemisphere, locations at �160°W, 60°W, and 60°EWestward-shifted seasonal base stated(AAM)/dt �0/weakened momentum sink shifting polewardMJO and fast component give large negative mountain torqueStrong subtropical jets over the Western HemisphereAsian–Pacific wave train favors anticyclonic wave break across east Pacific Ocean for transition to stage 1Heavy precipitation event possible across southwestern United States


Hemisphere, the positive mountain torque is producedby high pressure anomalies east of the Tibetan Plateauand cold air outbreaks that accompany the shift of con-vection to the west Pacific.

4. Summary and conclusions

We have proposed a synoptic–dynamic model of sub-seasonal variability that is useful for weather climatemonitoring and for medium-range prediction assess-

ment. The monitoring involves daily subseasonal vari-ability while the prediction focuses on forecast leadtimes from 3 days to 3 weeks. The GSDM is constructedfor the Northern Hemisphere cool season but the sameprocesses are active during the rest of the seasonalcycle. For example, to first order, the MJO circulationand convective anomalies merely shift northwest duringnorthern summer and become larger in the Southern(winter) Hemisphere. There is also a summer analog tothe stage 2 wave train seen in Fig. 13. The approach

FIG. 14. Zonal (contours and shading) and global (curves) anomalies obtained by lag regression onto the dailyrelative AAM tendency for November–March 1979–95. (a) Total AAM: contour interval is 0.1 � 1024 kg m2 s�1,left ordinate labels are for global curve in AAM units (1 unit � 1.0 � 1024 kg m2 s�1). (b) The flux convergenceof relative AAM: contour/shading interval is 0.2 Hadleys, left ordinate labels are Hadleys. (c) The frictional torque:same as in (b) but contour–shading interval is 0.1 Hadleys. (d) Same as in (c) but for mountain torque. Note thatthe contour interval in (b) is twice that in (c), (d). The right ordinate labels are latitude for the zonal contours.


discussed in section 3 will be applied to the other sea-sons in future work. Newman and Sardeshmukh (1998)provide some clues about the sensitivity of forcing andresponse during the course of the seasonal cycle.

By keying in on the global relative AAM tendency,the construction of the GSDM is made easier, althoughthe regional anomaly patterns and their relationshipsare blurred. A version of Fig. 13 (not shown) madefrom the lag regression of the 200-mb streamfunctionand OLR fields onto the daily AAM tendency supportsthe idea that the composite variations around day 0(stage 2) consist of different time scales of forcing,sometimes contributing to large global AAM tenden-cies. In our approach, we have defined the dominanttime scales that drive the global AAM tendency andthen the preferred phase relationships that give a largetime tendency. As a result, stages 2 and 4 contain aspecific phase of the fast time-scale component whereasonly general storm-track changes are invoked in stages1 and 3.

The GSDM is used in conjunction with the daily real-time monitoring of a broad range of weather climateindices, maps, and forecasts. These range from thelarge-scale patterns of SST down to ongoing barocliniclife cycles or tropical convectively coupled Kelvinwaves. The multiple time scales contribute to rapidtransitions of the tropical and extratropical circulation,which are difficult for operational GCMs to captureand can lead to large forecast errors. The 2001–02 casestudy examined two such transitions and their relation-ship to tropical forcing from two MJOs and midlatitudemountain torques. It highlighted a link between theMJO, extratropical wave trains, and baroclinic waveprocesses over the Pacific–North American region. Thetransition included a cyclonic (anticyclonic) wave breakthat ushered in strong (weaker) subtropical westerliesand a positive (negative) PNA.

An operational forecast model’s 11-day predictionshowed that the 3 periods of relatively low model skillin 150-mb streamfunction at 11 days occur when a ma-jor longitudinal shift of tropical convection is observedduring the period of the forecast. The model is moresuccessful at capturing the initial conditions of tropicalprecipitation and persisting them—a sometimes usefulattribute for the week 1 forecast. The relationship be-tween objectively defined “flare-ups” of convection andthe time evolution of predicted and observed fields willbe examined in a longer reforecast dataset in futurework.

The GSDM was developed to provide an additionaltool for the medium-range forecaster to assess the stateof the atmosphere–ocean at the initial time and therebyevaluate the predictions of numerical models. The

GSDM is being used in real-time weather climate dis-cussions and experimental week 1–3 predictions (avail-able online at http://www.cdc.noaa.gov/MJO/Forecasts/climate_discussions.html). Whether the GSDM can beused to improve subseasonal predictions on average re-mains to be determined. However, real-time weatherclimate monitoring within the framework of the GSDMshould help capture sudden shifts in tropical convectiveforcing and may improve the interpretation of numeri-cal model predictions of high-impact, extreme weatherevents.

Acknowledgments. Thanks to Brian Mapes and twoanonymous reviewers for their thoughtful and construc-tive comments on the paper. We thank Randy Dole forhis encouragement and support as director of the Cli-mate Diagnostics Center. Thanks to Dennis H. McCar-thy, Director of the NOAA/NWS Office of Climate,Weather, and Water Services, for supporting E. Berry’stemporary assignment to CDC to work on the paper.We also recognize Peter A. Browning, Chief of theNWS Central Region Headquarters MeteorologicalSciences Division, for supporting additional travel toCDC to finish the final manuscript and Larry Ruthi,Meteorologist in Charge for the NWS Weather Fore-cast Office, for allowing E. Berry the time and supportneeded to complete this project.

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